How can Cross Multiplication be intuited or pictured? average(average(a,b),c) vs. average(a,average(b,c)).

The two questions were closed as unclear because they're unclear. There's no dissimulation involved.

I don't see any evidence in r~~'s comment that they understood the question. They say that you've ignored suggestions elsewhere for how to improve it, and they reference the introduction, but that is in no way equivalent to saying that they understand what on Earth the apparently broken markup is supposed to signify.

A question should be self-contained. If it's been asked elsewhere better then look for the answer in that same elsewhere, bring your own question up to the standard of that better question elsewhere, or both. This applies for any value of "elsewhere", but bearing in mind that Codidact exists because of people choosing to boycott SE, it is doubly unreasonable to post a question in the form "Please answer this question on SE".

Peter Taylor understands my question faultlessly, but the hitch is that he doesn't know how to intuit this?

If your question is indeed "Why does dividing two equal things by the same thing give two equal things?" then ask that, delete the irrelevant pictures, and try to explain what you find unintuitive about it.

And please improve the existing post and ask for it to be reopened rather than posting a new question which asks the same thing, even if it does do a slightly better job of it.